Managing Buzz. October Abstract

Transcription

1 Managing Buzz Artur Campbell, Dina Mayzlin and Jiwoong Sin October 203 Abstract We model te incentives of individuals to engage in word of mout (or buzz) about a product, and ow a firm may strategically influence tis process troug its information release and advertising strategies. In te model individuals are privately motivated by a desire to signal teir type to oters. Individuals are eiter a ig or a low type, and during social interactions it is valuable for any individual to increase anoter person s posterior belief tat se is a ig type. We find tat a firm will restrict access to information by low types at te information release stage. We also find tat advertising may crowd out te incentives for consumers to engage in word of mout, and tat a firm can benefit from a credible commitment not to engage in advertising. Finally, we find tat te ability by te firm to target advertising to well-connected consumers may be detrimental to te signaling value of word of mout. Our model provides new insigts into te tradeoff a firm may face between spreading information quicly versus maximizing te total spread of information about te product. Keywords: Buzz, word of mout, self-enancement, signaling, advertising, diffusion. We tan Florian Ederer, Joannes Horner, Odilon Camara, seminar participants at Brown University, CKGSB, Columbia University, Indiana University, Monas University, Paris Scool of Economics, Purdue University, University of Cambridge, University of Florida, University of Melbourne, Yale University, SICS Conference at Bereley, and te Conference on te Economics of Advertising in Moscow. 35 Prospect St., P.O. Box , New Haven, CT 06520, artur.campbell@yale.edu, jiwoong.sin@yale.edu, USC Marsall Scool of Business, Los Angeles, CA 90089, mayzlin@marsall.usc.edu.

2 Introduction In July 20, te European music streaming site Spotify launced in te US maret. At first, its free US version was available by invitation only. Interestingly, obtaining te invitation was non-trivial, and direct invitations were limited to certain groups: consumers could receive one eiter troug current users or troug oter cannels. For example, te company sent invitations to users wo interacted wit Spotify on Twitter, and Coca Cola gave out invitations to users wo submitted teir address. After a few wees, anyone could download te free version of Spotify troug te company s website. 2 By November 20, Spotify was able to attract 4 million users, wile undertaing almost no advertising. 3 In te same mont Google launced its new social networ site, Google+, using te same invitation-only metod. Users could join eiter by receiving an invitation from Google or by receiving one from a friend. For a brief period in te summer of 20, receiving an invitation from Google+ became a status symbol. Here is wat Ken Hess wrote on te tec news site ZDNet on June 30, 20, Dear Google, I want a Google+ account. I m an avid Googler and ave always been an early adopter of all tings Google. Please give me an account before you give tem to anyone else on my list so I can gain some real street cred wit my fellow ZDNetters. 4 On October 20, Google announced Google+ s user base to be at more tan 40 million users. 5 Similarly to te Spotify example, media sources speculated tat te initial exclusivity surrounding te site contributed to early buzz and ig adoption rates. 6 Many mareting practitioners recommend and use similar strategies wic limit access to information in order to spur word of mout. For example, Huges (2005) states, Sometimes witolding can wor better tan flooding. Limit supply and everybody s interested. Limit tose in te now of a secret, tose not in te now want te currency of nowing - tey want to be part of te exclusive circle. David Balter, te founder of te buzz mareting firm BzzAgent, considers exclusivity to be one of te necessary ingredients for a successful word of mout campaign, Exclusivity is te velvet rope of social media: everyone wants to be special enoug to be on te rigt side of it. 7 Also, Sernovitz (20) observes tat Many people are more liely to tal about a product if tere is some ind of insider access or privileged status and provides a number of examples were firms use exclusiv- ttp://news.cnet.com/ _ /get-a-quic-and-easy-invitation-to-spotify/ 2 One possible reason for a firm s initial limited release could be a beta version of te product in a test maret for te purposes of collecting feedbac from users about te product s functionality before its wide release. Tis explanation is less applicable to te Spotify case given its presence and operational volume in Europe by te time it launced in te US maret in 20 Spotify ad already become te most popular suc service in te world and it ad.6 million paid subscribers and more tan 0 million registered users in total (ttp:// 3 ttp:// 4 ttp:// 5 ttp:// 6 See, for example, Spotify s ascension can be largely attributed to word of mout (ttp:// 7 ttp://blog.ubspot.com/blog/tabid/6307/bid/683/4-social-media-metods-for-generating-word-of-mout.aspx 2

3 ity strategy to increase word of mout about teir products. For instance, retailers sometimes offer private sopping ours for teir select customers te nigt before new products are available to te public, and software companies send prerelease versions of software to active message board users. One interesting aspect of tese strategies is tat tey seem to contradict te intuition tat wider exposure to product information will lead to more word of mout and a larger fraction of te population eventually olding te information. In tese examples, it is profitable for a firm to increase te number of people tat now information about teir product, yet tese firms adopt strategies to purposefully limit te number of people wo are initially exposed to product information. In tis paper we explore wy a firm tat is seeing to maximize te number of people wo possess information about its product may undertae strategies wic actively restrict early access to te information. Te firms empasis on word of mout management is driven by te recognition tat word of mout significantly impacts consumer purcase decisions. Word of mout as been sown to affect purcasing beavior in restaurant coices (Luca 203), boo sales (Cevalier and Mayzlin 2006), baning (Keaveney 995), entertainment (Cintagunta et al. 200), tecnological products (Herr, Kardes, and Kim 99), and appliances and cloting (Ricins 983). 8 However, teoretical models of word of mout largely ignore te incentives to engage in word of mout by treating it as a costless, mecanical process. Consequently, te existing literature offers little insigt into ow exclusivity may elp diffuse information via word of mout. A central issue for understanding a firm s exclusivity strategy in tis context is te motivation of consumers to acquire information and ten engage in word of mout about it. In tis paper, we address tis issue by modeling te motivation of individuals to engage in word of mout and treat te word of mout generation process as an outcome of strategic consumer beavior. We focus on a particular motive word of mout as self-enancement (Baumeister 998) or te idea tat an individual engages in word of mout to mae erself appear nowledgeable or trendy in a social setting. By explicitly modeling tis motivation of consumers to engage in word of mout, we sow ow exclusivity, troug restricting wo as access to information, affects te decision to spread word of mout and ow tese strategies increase te total diffusion of information. A main lesson from our analysis is tat a firm s strategy to generate word of mout is as muc about wo does not receive information as it is about wo does. We develop a model were consumers meet one anoter at a Poisson rate over time. Te ey element of te model is tat te utility an individual receives during a social interaction is an increasing function of er peer s belief tat se is te ig type (utility from self enancement ). Te most straigtforward interpretation of ig type is being nowledgeable about a particular product area or 8 Tese studies are also consistent wit recent industry researc: for example, according to Word of Mout Mareting Association (20), 54% of purcase decisions are influenced by word of mout. Also, Word of mout is te primary factor beind 20 to 50 percent of all purcase decisions in McKinsey Quarterly (Bugin et al. 200), and word of mout remains te biggest influence in people s electronics (43.7%) and apparel (33.6%) purcases, National Retail Federation (2009). 3

4 aving category expertise: for example, aving good taste in wine, being tecnologically savvy, nowing te best restaurants and bars, or aving good taste in music. Prior to meeting oters, individuals coose weter or not to acquire information about te firm s product at a certain individual-specific cost. Ten, during eac social interaction, individuals decide weter or not to engage in costly word of mout. We focus on a signaling equilibrium were word of mout serves as a credible signal of ig type. Te central focus of our analysis is ow te firm can manage te extent of te information diffusion in tis signaling game. We broadly consider two types of strategies by te firm. First, we consider information release strategies were te firm imposes differential costs for information acquisition on different types of consumers. Wen te costs of acquiring information for te low type are ig enoug, tere exists a signaling equilibrium were individuals acquire information and ten pass it on troug word of mout to people tey meet. As information diffuses in te population, and low social types acquire information troug word of mout, te signaling value of te information becomes diluted, and diffusion stops wen te signaling value is equal to te cost of engaging in word of mout. Hence, te firm can influence te extent of te diffusion by manipulating te asymmetry in te cost of acquiring information across different groups of consumers. Te optimal information release strategy of te firm is to maximally increase te costs of te low type and minimize te costs of te ig type. Tis enables us to explain wy exclusivity strategies by a firm tat restrict (in particular ways) wo as access to information about te product may in fact increase te total amount of information tat is sared in te population. We also igligt a basic trade-off between increasing te initial speed of diffusion and maximizing te total spread of information about te product: wile confining te initial spread of information to te ig types maximizes te incentive to tal on te part of eac exposed consumer, te diffusion process taes longer since te number of exposed individuals is small early on. Second, we introduce advertising by te firm and consider ow te ability of te firm to undertae advertising affects te incentives for consumers to acquire information and engage in word of mout. We find tat advertising by te firm crowds out te incentives of individuals to acquire information and engage in word of mout. Hence, a commitment by te firm not to engage in advertising can increase te diffusion of information. We sow tat a natural way for a firm to commit not to advertise is to release te information a sufficient amount of time prior to product release. Tis increases te present value of costs of advertising for te firm, tereby allowing word of mout to occur. Finally, we apply our model to a setting were te firm may target advertising at individuals wo are more connected (meet people more frequently) tan oters. Tis type of targeting strategy appears to be particularly attractive for firms because a significant increase in demand migt be possible wit limited budget. We find tat advertising wic is targeted in tis way tends to ave a particularly strong negative impact on te signaling value of information. Tis reduces te extent 4

5 of total information diffusion even conditional on an amount of information acquired by individuals. Unless an individual s meeting rate is correlated wit er own social type, simply reacing out to tose ig mixing individuals can displace te incentive to spread word of mout. Te rest of te paper is organized as follows. In te next section, we discuss te related literature, and Section 3 presents a model of buzz based on te self-enancement motive and analyzes ow a firm interacts wit tis motive to maximize te diffusion of information troug its information releasing strategy. In Section 4, we examine te effect of advertising on word of mout generation and Section 5 extends te model by allowing te eterogeneous mixing patterns among consumers. We conclude in Section 6. 2 Literature Review Our paper is most closely related to a number of papers in social networ teory tat study a firm s optimal strategy in te presence of learning or adoption externality troug some forms of local interactions by consumers, including word of mout. Typically, tese papers are interested in ow caracteristics of te social networ interact wit a firm s pricing (Galeotti 200, Candogan, Bimpiis and Ozdaglar 200, and Ifrac, Maglaras and Scarsini 20), or advertising strategy (J. Campbell 203, Galeotti and Goyal 2007, and Catterjee and Dutta 200), or bot (A. Campbell 203). Galeotti (200) is te most related paper. Te autor considers costly searc for pricing information by consumers in a model were two firms engage in Bertrand competition. Similarly to te current paper it is costly for consumers to acquire information directly. Differently, word of mout is costly for te receiver of information but it is not costly for te sender of information. In contrast we assume it is costly for te sender to pass on information but not for te receiver to receive te information. Te reason for tis difference in assumptions is tat te focus of te two papers are different. Te current paper is focused on te motivations of individuals wit information to engage in word of mout (te senders of information). On te oter and Galeotti (200) is concerned wit te equilibrium of consumer searc (te receivers of information) eiter directly or troug friends and firm pricing. Many of te oter papers in te existing literature ave detailed models of te social networ but treat word of mout generation as a mecanical process, wereby a consumer passes on information upon acquiring it, and te word of mout stops after a certain number of steps (or wit some probability after eac step). Galeotti and Goyal (2007) and J. Campbell (200) assume tat firms initially advertise to consumers and ten word of mout travels a distance of one in te social networ. 9 Catterjee and Dutta (200) assume te firm can pay individuals to engage in word of mout. Ifrac, Maglaras and Scarsini (20), Candogan, Bimpiis and Ozdaglar (200), and A. Campbell (203) 9 Galeotti and Goyal (2007) also extend teir untargeted advertising results to a generalized maximum distance. 5

6 consider settings were consumers pass on information if tey are prepared to purcase te product. Tis line of analysis as been successful at relating caracteristics of te social environment (suc as frequency of connections/interactions, distribution of friendsips, and clustering of friendsips between members of te population) to a firm s strategy. Given te assumption of word of mout as a mecanical process in tese models, any firm strategy wic increases te propensity of any consumer to old or pass on information will facilitate a greater amount of information diffusion. In contrast, our paper addresses te issue of wy individuals engage in word of mout about a firm s product by explicitly incorporating an individual s social motivation. Our social signaling mecanism for word of mout leads to novel insigts into ow a firm may increase te diffusion of information troug restrictions on information acquisition, advertising and te ability to engage in word of mout. Te firm will optimally impose restrictions in ways wic increase te signaling value of te information. In a more broad context, our wor is also related to a number of papers wic examine information diffusion troug endogenous (privately motivated) communication between individuals in social networs. Galeotti and Mattozzi (20) study competition between two political parties wen voters acquire information via bot advertising and word of mout. Te autors find tat ricer communication networs lead parties to disclose less political information, voters to be less informed and parties to adopt more extreme policy platforms. Calvó-Armengol, de Martí and Prat (202) consider endogenous communication in organizations and Stein (2008) considers ow far troug a population ideas spread. Also, Nieaus (20) analyzes wat type of information may be learned in an environment were local information saring is efficient but is not necessarily globally efficient. However, none of tese papers study te effect of exclusivity on te information diffusion. Our paper deals wit te incentives for individuals to engage in word of mout. Prior researc in psycology and mareting as proposed several distinct psycological motives tat can drive word of mout communication. For example, some studies ave found tat word of mout can be driven by altruism (Henning-Turau et al. 2004, Sundaram, Mitra, Webster 998), reciprocity (Dicter 966, Dellarocas, Fan, and Wood 2004) or te desire to signal expertise to oters (Wojnici and Godes 20). Altoug any of tese motives can independently drive word of mout, in tis paper, we focus on te latter desire to signal to oters about oneself in a social setting. Te starting point of our model is tat consumers derive benefits during social interactions from maing temselves loo good. Tis assumption is motivated by te psycological teory of self-enancement or te tendency to affirm te self (Baumeister 998, Fise 200, Sediides 993) and includes te tendency to draw attention to one s sills and talents (Baumeister 998, Wojnici and Godes 20). A number of papers provide empirical evidence tat word of mout is influenced by motives related to self-presentation (Berger and Milman 20, Berger and Scwartz 20, Hennig-Turau, et. al. 2004, Sundaram et al. 998, Wojnici and Godes 20). Berger and Milman (20) find tat positive content is more liely to be sared, as is content tat evoes ig-arousal emotions. Te 6

7 autors conjecture tat te saring of positive content may be due to impression-management. Berger and Scwartz (20) find tat, in te sort run, conversations are influenced by ow interesting te product is: consumers do not want to appear to be dull. In a survey conducted by Hennig-Turau et. al. (2004) respondents indicate self-enancement as one of te primary motivations beind word of mout. Also in a survey, Sundaram et. al. (998) find tat 20% of positive word of mout is undertaen to sow connoisseursip, to project temselves as experts, to enance status, and to see appreciation, and Wojnici and Godes (20) sow in a series of experiments tat experts are less liely to tal about teir negative experiences in an attempt to enance teir self-image since a negative outcome reflects badly on teir ability to mae coices. Finally, our model studies ow social interactions between consumers can be influenced by a firm s strategy. Pesendorfer (995) analyzes te interaction between a firm s design innovation and pricing strategy and consumers social matcing beavior. In is model, owning a particular product serves as a wealt signal for a consumer to oters tat tey are a ig type. Tis is valuable for ig types to identify one anoter during a matcing process. Altoug bot te current paper and Pesendorfer (995) consider social interactions between consumers, our focus is very different as we consider ow a firm s information release and advertising strategy interacts wit tese social concerns (in particular, te effect of exclusivity on information diffusion) wereas te focus of Pesendorfer (995) is on product cycles and pricing. Yoganarasiman (202) also models a fasion firm s desire to witold te identity of its ottest product in order to enable consumers to signal to eac oter tat tey are in te now in social interactions. Our paper is similar to Yoganarasiman (202) in tat bot model te firm s incentive to restrict information in communication strategy to facilitate te social interaction. However, Yoganarasiman (202) analyze te firm s pricing strategy to extract consumer surplus in a static setting wile we focus on te effect of initial exclusive release on te extent of information diffusion in a dynamic setting. 3 A Model of Buzz 3. Model Set-up A monopolist sells a product to a mass of consumers. A consumer i may be one of two types: ig or low =, l were Pr [ i = ] = < 2 (ig types are relatively scarce). Consumers are privately informed of teir own type. Te ig type consumers are more nowledgeable about te product category, and tis is viewed positively by all te consumers. In social situations, it is valuable for eiter type of person to be perceived as te ig type by oters (self-enancement motives). One can tin of te ig-type consumers are being broadly nowledgeable about te product category (wine entusiast, tecnology savvy, nows all te fasionable/trendy restaurants and bars). Importantly it is valuable to be perceived as a ig-type, regardless of te consumer s true type. 7

8 We assume tat te firm s profit is linear in te fraction of consumers wo obtain information about its product. 0 Te reduced form of te firm s objective is to maximize te fraction of te population wic receives a piece of information m about its product. We denote te fraction of te population tat as received te information at time t by S(t). Initially we assume no advertising before introducing it in Section 4. Witout advertising consumers can obtain te information in two ways. First, tey may undertae costly searc to learn about te product temselves. Second, tey may costlessly ear about te product from anoter person. Once a consumer as found out about te product troug eiter cannel, se too is able to pass on te information to oters. Our focus in tis paper is to study ow far te information eventually diffuses troug te population wen passing it on is costly to consumers. Timing At time t = eac individual cooses weter to obtain information m about a firm s product. We assume tat tis information is ard and verifiable: a consumer is not able to fabricate information. Tere is a fixed lower bound on te costs for obtaining information for eac consumer, c i, wic is i.i.d. uniformly on [0, c]. One can tin of tis as te minimum amount of time and effort an individual must expend to understand te information. Te firm, in addition to tis cost, may impose furter costs on eiter or bot types troug its information release strategy. Tis is modeled as an additional cost, l 0 wic is type-specific (tat is, te total cost tat an individual i of type = {, l} bears to obtain information about te product is c i + v ). We assume tat imposing a type-specific cost is costless (or involves a very small cost) for te firm. For example te firm can explicitly increase consumer information acquisition costs troug te use of tecnical jargon wic te ig type more easily understands, or, equivalently, can decrease te cost of te ig type relative to te low type, troug releasing information on blogs, at events, or in venues tat are frequented by ig types but not low types. Wat is important for te model is tat te firm 0 Altoug we leave te firm s objective in tis reduced form in our main text, one could also model tis reduced form. Te firm s product is produced at marginal cost c and is ex ante equally liely to be one of n types. Consumers are also one of n types; eac type values te corresponding product at #>cand values te oter types at 0. Tere is an equal mass of eac consumer type in te population. Suppose tat c> #. Absent receiving information, no consumer n will purcase te product at any price p> # and te firm will not sell at a price p<c. However, any consumer tat n receives information about te type of te product will purcase it if it matces teir preferred type at p apple #. Te firm maes a profit of # c per consumer wo receives information, tus te firm s profit is linear in te fraction of n te population wo receive information about te product. Note also tat te firm captures all te surplus from te purcase and so te information is not valuable to a consumer in its own rigt. We study a setting were te firm captures te full surplus from any sale so as to isolate te incentives of individuals upon acquiring te information to pass it on to oters. We tin our model fits particularly well many entertainment, tecnology and fasion product categories were being perceived as nowledgeable about tese areas is desirable. In tese cases, it would be natural to assume tat tese costs would be iger for te low type tan te ig type. However, we do not do tis because tis assumption is not a necessary condition to find tat te firm as a strict incentive to treat eac type asymmetrically troug its information release strategy. 8

9 may differentially affect te costs of eac type, and tat tese costs are common nowledge. Using te Spotify example, te firm created an asymmetry in acquisition costs by posting te invitation to register on its Twitter feed. Hence, all consumers could potentially obtain te invitation, but te cost of acquiring it is lower for te tec-savvy consumers wo are already familiar wit Twitter. Anoter prominent example of tis occurs wen tecnology companies suc as Apple or Samsung mae product announcements at events, wic are broadcast troug live feeds. Again in tis instance tec-savvy individuals ave lower costs to find, monitor and even understand tese sources. Tus being able to engage in word of mout about te information serves as a signal of an individual s tec-savvy. From time t =0onwards individuals meet oters at rate in continuous time. During eac meeting an individual, wo as acquired te information previously, may pass on te ard information m at a cost, were we assume <<, or pass on no information? at zero cost. We assume tat tis is done simultaneously during te meeting so tat eac individual as te ability to do so witout seeing te oter individual s information first. Utility during social interactions A central element of our model is tat individuals derive a benefit from word of mout due to selfenancement. We capture tis idea troug a social utility U ij,tatanindividuali receives from an interaction wit anoter individual j, were te utility is an increasing function of te beliefs te oter consumer as about te focal consumer s type. In particular, consumer i receives instantaneous utility U i (b j ( i = m, t)) if consumer i passes a message m at time t, were b j ( i = m, t) is te oter consumer j 0 s belief tat consumer i is a ig type upon receiving te information m. similarly, U i (b j ( i =?,t)) if te consumer does not pass information, were b j ( i =?,t) is te belief if no signal (denoted by?) is sent. Given our notions of ig and low types, we assume du i db j > 0. Also note te signaling benefit at a time t is And U i (t) =U i (b j ( i = m, t)) U i (b j ( i =?,t)) () wic is te difference between sending a signal and not sending a signal at tat time t. Weassume tat utility is linear in beliefs; tus, U (b j ( i = m, t)) U (b j ( i =?, 0)) (2) = u [b j ( i = m, t) b j ( i =?,t)] were we normalize ū =. We assume tat an individual passes on information only wen U i (t) >. 2 2 Tis procludes equilibria were only a fraction of individuals wit te information coose to pass it on due to indifference and tese fractions appen to differ in suc a way across types tat U i (t) = is maintained over time. 9

10 Finally note tat we assume tat te firm extracts te entire consumer surplus from te sale of te product to a consumer, see footnote 0. Tus, tere is no value from obtaining information for te purposes of maing a purcase decision. Tis setup allows us to only focus on te utility tat te consumer derives from te information, wic is accomplised troug signaling. 3.2 Analysis We focus on a signaling equilibrium were consumers engage in word of mout in order to signal to eac oter tat tey are a ig type. We focus on equilibria were individuals engage in word of mout wile te signaling benefit is strictly greater tan te costs of passing on information. 3 We analyze ow te fraction of eac type wo acquires information at t = determines te total amount of information diffusion. We denote te fraction of eac type wo becomes informed at t = by ',' l. Tese are going to be endogenously determined in equilibrium, but for now we tae (',' l ) (wic we denote by ~ ') as given. For te moment, we also assume tat ' >' l (wic will be confirmed in equilibrium subsequently). Te initial condition of te informed population at t =0 is S 0 = ' + ' l ( ) and te rate of growt of te informed population is given by: ds dt Tis results in te following pat for S (t): S (t) = wic continues to grow wile word of mout is taing place. diffusion (wen S(t) stops growing) below. = S (t)( S (t)) (3) +ae t, were a = S 0 S 0 (4) We caracterize te extent of te Next, we caracterize te evolution of consumers belief over time wile individuals wit te information engage in word of mout. Beliefs At t =0, consumers beliefs are b j ( i = m, 0, ~')= ' ' + ' l ( ) (5) We feel tese types of equilibria are unreasonable since tey arbitrarily introduce an asymmetry between te types by manipulating indifference in a very specific manner. Furtermore te extent of diffusion found in tis way is not robust to incorporating individual specific costs of passing on information wic are draws from [, + ] were is arbitrarily small. In te equilibria we analyze all individuals wit information act in te same way, tey eiter all pass it on or do not. 3 Te equilibrium is semi-separating at all times t>0 until te word of mout and te information diffusion stop. At times wen word of mout is taing place te belief about a consumer s type is only a function of te relative fractions of ig and low types wic ave te information at tat time. 0

11 and b j ( i =?, 0, ~')= ( ' ) ( ' ) +( ' l )( ). (6) Beliefs cange over time as te message diffuses troug te population. Te Bayesian belief on te sender s type wen a consumer receives a signal at a time t (receives word of mout) is given by: b j ( i = m, t, ~') = S (t) S 0 S (t) [b j ( i =?, 0, ~')] + S 0 S (t) [b j ( i = m, 0, ~')] (7) = b j ( i =?, 0, ~')+ S 0 S (t) [b j ( i = m, 0, ~') b j ( i =?, 0, ~')]. Te belief on te sender s type upon not receiving a signal is: b j ( i =?,t,~')= ( ' ) ( ' ) +( ' l )( ) = b j ( i =?, 0, ~'). (8) Note tat te and l type are equally liely to ear (or not to ear) about te product troug oters word of mout for any t te same over time. 0. Hence, te belief on te consumer s type, conditional on no signal, is Extent of diffusion We focus on equilibria were te diffusion of te information stops at a time t wen te marginal value of signaling equals te marginal cost of passing on te information. 4, 5 Tis allows us to describe all consumers decision about weter to pass on te information, conditional on aving acquired it, by te time t at wic consumers stop passing on information. Te instantanous signaling value at t is: U (t) =U (b j ( i = m, t, ~')) U (b j ( i =?,t,~')) (9) = S 0 S(t) [b j ( i = m, 0, ~') b j ( i =?, 0, ~')] S(t) is strictly increasing over time and tus te instantaneous signaling benefit of signaling strictly decreases over time. Tat is, as information diffuses troug te population, and more low types receive information troug word of mout, te signaling value of passing on information decreases. Under our assumption tat << word of mout is exactly equal to te cost of transmission tere exists a time t wen te instantaneous benefit of U(t )= at wic point word of mout 4 Formally we require tat in equilibrium individuals pass on information at all times s apple t wile lim r!t U (r) > and stop at any time t were lim r!t U (t )=. 5 Tis assumption rules out equilibria wic stop at an arbitrary moment or from stopping and restarting troug appropriately specifying off-equilibrium beliefs. It also rules out equilbria were word of mout continues to occur by maintaining indifference amongst tose wo old te information U = and appropriately specifying fractions of eac type to pass on and not pass on te information.

12 stops. 6 Hence, te extent of diffusion is S (t )= S 0 [b j ( i = m, 0) b j ( i =?, 0)] (0) We first examine ow te extent of information diffusion depends on te fraction of ig and low types wo acquire information. Proposition. Te total information diffusion is increasing (decreasing) in te fraction of ig (low) types wo acquire information: ' < respectively. ds (~' ) d' 0, ds (~' ) d' l apple 0 were te inequalities are strict if ' l < and From Equation (0) we can see tat te total diffusion is te product of te proportion of te population wo acquire te information (S 0 ) and te instantaneous signaling benefit (b j ( i = m, 0) b j ( i =?, 0)) att =0. Te latter term can also be interpreted as te informativeness of word of mout as a signal of type; tat is te difference in te posterior belief following a message versus no message. Increasing ' increases bot te inital spread of information and te informativeness of word of mout as a signal. Hence, te total diffusion of information is increasing in '. Similarly, decreasing ' l increases te informativeness of word of mout as a signal of type. However, decreasing ' l also decreases te initial spread of information. In our model, te former effect dominates te latter: te diffusion of te firm s message is decreasing in ' l. Hence, increasing te initial asymmetry between te two types benefits te firm in te long run by maximizing te over-all diffusion of information. An immediate result of te Proposition is tat te diffusion of information is maximized at ' =and ' l =0in te partial equilibrium were we do not consider te incentives for consumers to acquire information at t = full equilibrium.. Next, we sow tat maximal asymmetry remains te optimal solution in te Consumers Incentives to Acquire Information We solve for te perfect Bayesian equilibrium of te model by solving for te consumers decision to acquire product information at t =. Te decision to acquire te information at t = depends on te total signaling benefit of word of mout during te diffusion process. If tis benefit is greater tan an individual s cost c i, ten te consumer will acquire information. For simplicity, we assume no time discounting for consumers. 7 Denoting te time at wic te diffusion process ends by t,te 6 We restrict our analysis to strict equilibria. For t t (~' ), wordofmoutdoesnotoccur. Aslongasteout-ofequilibrium belief is suc tat b j ( i = m, t) <b j ( i = m, t (~' )) for all t t (~' ), consumers prefer not to spread word of mout upon reacing t (~' ). 7 None of te results inge on tis assumption. Te instantaneous signaling utility at time t decreases as information diffuses in te population. Adding time discount furter reduces tis instantaneous utility, but does not cange our main results. 2

13 total signaling benefit for an agent is ten 8 V = ˆ t 0! S (t) ( U (t) ) dt S 0 () were te first term S(t) S 0 is te probability of remaining uninformed at time t for an individual uninformed at time 0 and te second term, U (t), is te signaling benefit at eac moment of time. We can furter simpify te expression to obtain te following: 9 S S 0 V = +ln S 0 S 0 S 0 S Here te total signaling benefit is expressed as a function of only te initial diffusion state (S 0 ) and te total extent of information diffusion (S ), bot of wic are functions of ',' l. Tus, V = V (! ' ). As we stated previously, te firm can increase te costs of te ig and low types for acquiring information by l 0 and 0 to create asymmetry between two types, enabling a signaling equilibrium were word of mout can serve as a signaling device. At t = (2), te customer i of type cooses to acquire information if c i + v apple V (! ' ). Since c i is assumed to be i.i.d. uniformly on [0, c], te proportion of consumers of type wo coose to acquire information is 8 0 if V v >< < 0 ' = (V (! ' ),v )= V v c if 0 apple V v apple c >: if V v > c Note tat te relationsip between v and ' is not one-to-one at te extreme ends of ' and we assume tat if (V (! ' ), v )= (V (! ' ), ṽ ) for v apple ṽ, te firm cooses v. (3) 3.3 Optimal Information Release Strategy Te firm s optimization problem is max, l S (~' ) 8 More precisely, te total signaling benefit is te difference between te expected benefit wit and witout information at t =. Te expected benefit wit information at t = is W acq t (~' )=. ( U (t) ) dt Even if 0 te consumer does not acquire te information initially, se may still acquire it troug oters word of mout and terefore, te expected benefit witout information at t = is W no acq t (~' )= S(t)( S(t)) t 0 S 0 ( U ( ) )d dt = t t ( U (t) )[S(t) S0]dt. Terefore, te total signaling benefit for an agent is V = W no acq S 0 (~' ) W no acq (~' )= 0 t ( U (t) )(( S0) [S(t) S0])dt = t ( S(t)) S S 0 ( U (t) )dt. 9 We do so by maing a cange of variables for dt, ds = S (t)( S (t)), dt = ds dt S(t)( S(t)) 3

14 subject to ' = (V (! ' ),v ) ' l = (V (! ' ),v l ) 0 l 0 Before finding te optimal strategy for te firm, we note tat asymmetry is a necessary condition for word of mout to tae place. Lemma. No word of mout occurs under symmetric costs. Te underlying driver for te word of mout diffusion is te signaling benefit wic arises from te asymmetry between te ig and low types (' >' l ) in Equation (0). It is obvious tat under symmetric costs (wic leads to ' = ' l ), S =0. Terefore, no word of mout arises. Te following Proposition caracterizes te optimal strategy (optimal level of asymmetry) tat maximizes information diffusion in te full equilibrium. Proposition 2. Te optimal strategy for te firm is to set a sufficiently large cost for te low type suc tat ' l =0,andminimizetecoststoteigtype, + ln + ln ' < if c and ' =if c<. =0suc tat 0 <' apple. Moreover, We find tat te optimal strategy is to restrict information to te low-type consumers by setting te cost of information to be ig wile minimizing te costs for te ig-type consumers. result demonstrates tat te firm benefits from maximal asymmetry in initial information acquisition between te two types. In te model, it is not only te costs of a given individual but also te costs of oters tat provide te incentive to engage in word of mout and to acquire/learn information about te product in equilibrium. A firm can manipulate tis asymmetry by foregoing opportunities to decrease te costs of te low type or even increasing te costs of tis type, troug ow and wat it communicates, and were it maes available information about its product. Tese types of activities are ard to rationalize in te more mecanical models of word of mout. Tis igligts te importance of including te motivation of consumers wen analyzing a firm s optimal strategies in tese environments. We also note tat our self-enancement mecanism is consistent wit many of te product categories were we tend to observe significant word of mout occurring, suc as fasion, entertainment and dining. From casual observation tese are also categories were it is often perceived to be desirable to be nowledgeable about products in tese categories. Clearly, waiting for information to spread troug word of mout taes time, and te firm may not be in a position to be patient. For example, a newly-released movie typically stays at a multiplex Te 4

15 cinema for only one to tree wees, and tus te timing of te information diffusion as well as te amount of diffusion can be critical. We revisit te firm s optimization problem wit te discount factor t =exp( rt), were r is te discount rate. In tis case, te firm s objective function becomes: max, l ( S (0) + ˆ t 0 ) ds dt e rt dt We find tat wen te firm is not too patient (r is sufficiently large), it may want to disseminate te information even to te low type customers by coosing a low enoug l suc tat some low types acquire information (' l > 0) to acieve a iger level of information diffusion at an early stage. Proposition 3. Wen te discount rate r is large enoug, te firm may coose an intermediate level of costs for te low type suc tat ' l > 0. Te Proposition demonstrates te tradeoff a firm may face between spreading information quicly versus maximizing te spread of information: by confining te initial acquisition of information to ig type consumers only, it maximizes an individual s incentive to engage in word of mout but te process of information diffusion taes a longer time. On te oter and, by allowing some low types to also gain access to te information te firm may acieve a greater level of initial adoption. However te incentives to engage in word of mout are reduced and te final extent of te information diffusion is smaller. Wen te firm is sufficiently impatient, it prefers to initially allow te information to be more widely accessible to consumers tan to wait for a wider diffusion by furter restricting access to information. Tis trade-off is illustrated in Figure. Allowing some low types access to information ( telling more people ) dilutes te signaling value of word of mout (te upper grap in Figure ) and results in sorter period of diffusion (t <t ) and a lower level of over-all diffusion (S <S ) compared to te case of telling few people (only ig types access to te information). However, it does yield a iger level of early diffusion (S 0 0 ), wic may be particularly valuable to te firm. 4 Advertising In Section 3, we find tat te firm optimally restricts initial access to information in order to increase word of mout among consumers. In tis Section, we sow tat attempts by te firm to jump-start te diffusion process troug traditional mareting actions suc as advertising lowers te signaling value of word of mout to te consumer. As a consequence, rusing diffusion troug advertising crowds out te incentives for individuals to acquire information. We add to our basic set-up in Section 3 a simple advertising tecnology, wic is costly to te firm, tat exposes consumers early on to information about te product. Here, we simplify te exposition by reverting to te setting wit no discounting and by assuming tat te firm cooses and l optimally suc tat =0and l is large so tat 5

16 belief b ( m,0) i b ( m,0) i Tell few people Tell more people S() t t =0 t* t** t S ** Tell more people S * S 0 S 0 t =0 t* Tell few people t** t Figure : Tradeoff between Spreading Information Quicly versus Maximizing te Total Spread ' 0 and ' l =0. Timing At t = consumers coose weter to searc for information. At t =0te firm exposes a fraction of te consumer population to te advertising message about te product, 20 and from ten on consumers engage in word of mout as before. Advertising is costly to te firm: C ( ) 0,C 0 ( ) >,C 00 ( ) > 0 for all 0. Our assumption tat te marginal cost of advertising at =0is greater tan implies tat advertising absent word of mout is not wortwile for te firm. We assume tat consumers only observe weter tey temselves receive (a i =) or do not receive (a i =0)tead; tat is, te firm s total advertising spending ( ) is not observable to te consumers, wo rater infer it in equilibrium. 2 Te word of mout generation process tat occurs at t>0 is te same as in Section 3, wit te only exception tat consumers inference and optimal stopping strategy is now also conditional on teir belief on te level of advertising undertaen by te firm. 20 We model advertising as a one-time pulse is for simplification purposes. We discuss alternative assumptions suc as a continuous advertising tecnology wic gradually informs people over time and alternative timing suc as te advertising occuring at or prior to t =. 2 Our main result in tis section sows tat commitments by te firm not to undertae advertising are valuable and result in a larger diffusion of information. Importantly we do not assume tat consumers can observe tat a firm as not advertised to anyone in te entire population. We feel it is reasonable to avoid tis assumption but we also note tat it is important. Suc an assumption would be equivalent in our model to te firm aving te ability to commit to undertae zero advertising. 6

17 Caracterizing te Word of Mout Signaling Equilibrium in te Presence of Advertising We solve for a Perfect Bayesian Nas equilibrium were, as in te earlier section, te diffusion of te information stops wen te marginal value of signaling equals te marginal cost of passing on te information. We focus on te signaling equilibrium wic results in te largest diffusion of information subject to te refinements described below. Te equilibrium is described by te firm s and consumers n o strategies {',, i } and teir beliefs i(a i ),b j ( i = m, t),b j ( i =?,t). Here, ' is te fraction of ig-type consumers wo coose to searc for information at t =, is te optimal level of advertising undertaen by te firm at t =0,and i is te equilibrium stopping time of word of mout. Te set of beliefs consists of () i (a i ), te consumers belief on te amount of advertising undertaen by te firm, wic is conditional on te consumer s personal exposure to advertising, a i, and (2) b j,j0 s belief on i s type following a social interaction wit i at time t during wic i eiter does or does not pass on information. In any equilibrium were 0 < < receiving or not receiving an ad are bot consistent wit te firm s equilibrium strategy. Tus a consumer s beliefs are te same in bot scenarios i (a i = 0) = i (a i = ) =. For example, if te consumer believes tat te firm sent out an ad to 0% of te population, te fact tat se did or did not receive an ad does not cange er prior belief. In contrast, in te case of =, not seeing an ad (a i =0) is not on te equilibrium pat, as is te case for =0 and exposure to te ad (a i =). In tese instances we impose a trembling and refinement on te set of equilibria, wic is defined in more detail in Appendix B. We assume tat tere is a tremble associated wit advertising. Tat is, wen te firm cooses a level 2{0, }, te actual fraction tat receive te advertisement is ( )+ ( )= + 2.Wesowtattelimit! 0 of tese trembling equilibria corresponds to te signaling equilibrium we find ere. As before, if tere are multiple solutions to te consumer s problem, we assume tat te firm can implement te solution wic results in te greatest level of information diffusion. Te beliefs are Bayesian on te equilibrium pat for t apple and satisfy b j ( i = m, t) b j ( i =?,t) <for all t> + ln. Finally, we maintain te assumptions tat c, wic guarantees tat not all te ig social types acquire information in equilibrium, and 2, wic is a sufficient condition for uniqueness of an equilibrium in te continuation game from t 0. We require uniqueness in order to undertae comparative static analysis of te firm s costs of advertising on te equilibrium. 4. Word of Mout Signaling Continuation Game (t 0) First, we solve te game beginning wit te consumer-to-consumer word of mout signaling game tat occurs after advertising exposure at t =0. 7

18 Consumers Word of Mout Decision Wen te firm engages in advertising te inference a consumer maes from an individual passing on information depends on bot te level of information acquisition ' and te beliefs of consumers about te level of advertising undertaen by te firm. In particular, affects ow te signaling value of information information until U (t) evolves over time, and ence ow long consumers will continue to spread te U (t) =. We denote te consumers inference of te fraction of te population wit information about te product due to searc and advertising at t =0by S 0, and te consumers inferred level of total information diffusion, by S c. Te lengt of time consumers engage in word of mout ', is given by ', = S c S0 ln (4) S c S 0 Te term S 0 is increasing in te conjectured level of advertising: S 0 ', = ' + (( ' ) + ) Te effect of advertising is to increase te initial fraction of population wit information at t =0from S 0 = ' in te basic model wit no advertising (were ' l =0)to S 0 = ' + (( ' ) + ) in te model wit advertising. Note tat te consumer-to-consumer signaling game troug word of mout remains te same as in te basic model, wit te only difference te initial level of exposure prior to word of mout diffusion. Te conjectured level of total diffusion S c (', ) is determined by wen consumer beliefs result in te signaling value of passing on information being equal to te cost of passing on information U (t) =. Interestingly, for a given level of initial information acquisition by consumers ', te consumers conjectured level of total diffusion is independent of te consumers conjectured level of advertising, providedtat is not so large tat no word of mout taes place ( < ' ( ' ( ' ) ) ' ). Lemma 2. For a given amount of initial information acquisition troug searc (' ), te consumers conjectured level of information diffusion ( S c )isindependentofteamountofteconjecturedlevelof advertising ( ) for all 0 apple apple : S c (', ) = S c (', 0). Te incentives to engage in word of mout at any point in time is governed by te signaling value of te information. Te signaling value in turn is determined by te initial asymmetry in information acquisition between ig and low type consumers, and te number of consumers of eac type wo ave acquired te information subsequently troug word of mout or advertising. Terefore, for a given level of initial information acquisition troug consumer searc, bot advertising and word of mout affect te signaling value by diffusing te information troug te population. Te mecanics of diffusion is te same across advertising and word of mout; in bot information cannels individuals are 8

19 informed randomly - individuals receive information irrespective of teir type. Since bot advertising and word of mout reduce asymmetry between ig and low types in te same way, advertising as te same diluting effect on te signaling value of information as word of mout. Hence, te evolution of te consumer s belief, as a function of te set of people wo are informed, is te same wen diffusion occurs troug eiter cannel. Advertising is a pure substitute for word of mout, wic stops at te point were U (t) =. Tat is, conditional on a given ', consumer s beliefs do not affect te conjectured extent of information diffusion, S c. Altoug te conjectured level of advertising does not affect te extent of information diffusion, it does affect te duration of word of mout. Lemma 3. For a given amount of initial information acquisition troug searc (' ), te duration of word of mout is decreasing in te conjectured level of advertising: d d < 0. Te conjectured level of advertising as no direct effect on te extent of te diffusion S c and tus as no effect on troug tis term. Te only effect comes troug te initial level of information S 0 (', ) wic is increasing in. Te time ', is strictly decreasing in S 0 and is tus strictly decreasing in te conjectured level of advertising. Firm s Advertising Decision Te firm cooses an optimal level of advertising spending wic maximizes te firm s conjectured level of diffusion S f. Tis conjectured level of diffusion depends on te firm s conjecture of te lengt of time consumers engage in word of mout, te fraction of ig types wo acquire information ', and its own level of advertising: Te function S f (', S 0 (', (', ) = arg max S f (',, ) C ( ), 2[0,], ) can be written in terms of te actual level of initial information acquisition ) and te conjectured amount of time consumers will spread information S f (',, ) = +ae, were a = S 0 (', ). (5) S 0 (', ) For a given level of initial information acquisition by consumers ', a firm is able to influence S f troug advertising activity wic canges te informed sare of te population S 0 (', ) at t =0. Lemma 4. Wen te marginal cost of advertising C 0 (0) is not too large, 22 tere exists a cutoff ˆ suc tat for all 0 apple apple ˆ, te optimal level of advertising is =0, and for all ˆ, tefirm s optimal coice of advertising is > > If C 0 (0) is too large te firm never advertises suc tat =0for all 0. 9

20 Te actual amount of advertising does not affect te lengt of time tat word of mout occurs because it is not directly observable to consumers. Te lengt of time is only affected by consumers own expectations of te level of advertising in equilibrium. Tus, advertising increases te number of individuals engaging in word of mout for a fixed amount of time. Hence, wen te conjectured lengt of time is smaller tan a cutoff, it is not optimal to undertae any costly advertising. Te firm will only undertae a strictly positive amount of advertising if its conjecture is above tis level. Moreover, in te case were advertising is positive ( > 0), te best response function is increasing in te conjectured amount of time consumers engage in word > 0 and satisfies te first order condition C 0 ( )= d S f d = d S 0 d. Here, te second equality relationsip follows from te observation tat advertising only affects te level of diffusion troug te level of information S 0 at t =0. Given te actual level of information acquisition ', and te firm s conjectured lengt of time tat consumers will engage in word of mout, te firm cooses an optimal level of advertising tat balances te marginal costs of advertising C 0 ( ) against te marginal impact on te firm s conjectured level of diffusion d S f d. Next, we find te equilibrium of te word of mout signaling continuation game (t 0). Equilibrium of te Word of Mout Signaling Game t 0 Te equilibrium of te continuation game for a given level of information acquisition is a pair of strategies { (' ), (' )} = { (', (' )), (', (' ))} and beliefs,b j ( i = m, t, ', ),b j ( i =?,t,' n Te firm and consumers coose best responses to eac oter s actions and beliefs are correct.. Proposition 4. For a given level of information acquisition ',tereisauniquepbne{ (' ), (' )} for te word of mout signaling game t We furter caracterize te equilibrium of tis continuation game for a given ' in te following lemma. Lemma 5. For a given level of information acquisition ',considertwocostfunctionsofadvertising C and C 2 were C 0 <C0 2.Wentemarginalcostsofadvertisingarelarger,televelofadvertising is lower and te lengt of diffusion is longer : (' ) 2 (' ) and t (' ) apple t 2 (' ). In equilibrium, bot te firm and te consumers correctly anticipate te equilibrium extent of diffusion S (' ),tus S c (', )= S f (',, )=S (' ). We also note tat for a given level of information acquisition ', te equilibrium level of advertising does not cange te equilibrium extent of diffusion S (' ), wic would ave been reaced witout advertising. Consumers expectations of te level of advertising are correct in equilibrium and from Lemma 2, S c (', 23 On te equilibrium pat, beliefs are pinned down by Bayesian beliefs; owever, any beliefs suc tat b j ( i =?,t,', )= and b j ( i = m, t, ', ) b j ( i =?,t,', ) apple for t> are possible. ) is 20

21 independent of. Terefore, te equilibrium extent of diffusion S (' ) is independent of te level of, and only depends on te level of initial information acquisition of consumers '. b ( m,0) j i belief b ( m, t) j i b ( m,0) j i belief b ( m, t) j b (, t ) j i St () b (, t ) t 0 t* 0 j i St () t** t * S * S 0 (a) Witout advertising t t* 0 t** t* (b) Wit advertising t Figure 2: Te Effect of Advertising on Word of Mout and Diffusion, given '. Advertising does not cange te extent of total diffusion S, but it expedites te diffusion process by increasing te initial level of informed individuals at t =0from ' to ' + (( ' ) + ). Tus, te word of mout reaces te level of S at wic individuals stop spreading te information (i.e., b j ( i = m, t) b j ( i =?,t)=) earlier wit advertising tan witout advertising (t <t ). Figure 2 illustrates te difference in information diffusion wit and witout advertising conditional on a given level of information acquisition. Te top two panels sow te evolution of beliefs over time. In bot cases, we see tat te diffusion stops wen te difference in beliefs is equal to. It also sows tat advertising clearly dilutes te signaling value of information by randomly distributing information to more consumers, wic reduces te asymmetry in information spread between ig and low types at t =0. But it does so exactly te same way as would oterwise ave taen place troug word of mout and tus, beliefs are lower at eac moment in time. Hence, advertising does not cange te extent of total information diffusion (S ), but te diffusion occurs for a sorter lengt of time. We empasize tat tis result olds for a fixed level of information acquisition '. In te full game, were te level of information acquisition is endogenous, advertising will affect te ex ante incentive for consumers to acquire te information, and tus te level of information acquired by consumers at t =. Tis, in turn, affects te extent of total information diffusion (S ). 2